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A new formulation of a spray dispersion model for particle/droplet-laden flows subjected to shock waves

Published online by Cambridge University Press:  28 October 2020

G. Gai Open the ORCID record for G. Gai [Opens in a new window] ,
O. Thomine Open the ORCID record for O. Thomine [Opens in a new window] ,
S. Kudriakov Open the ORCID record for S. Kudriakov [Opens in a new window]  and
A. Hadjadj Open the ORCID record for A. Hadjadj [Opens in a new window]
G. Gai
Affiliation:
DES-DM2S-STMF, CEA, Université Paris-Saclay, Paris, France CORIA, UMR-6614, CNRS, INSA, University of Normandy, 76000Rouen, France
O. Thomine
Affiliation:
DES-DM2S-STMF, CEA, Université Paris-Saclay, Paris, France
S. Kudriakov
Affiliation:
DES-DM2S-STMF, CEA, Université Paris-Saclay, Paris, France
A. Hadjadj*
Affiliation:
CORIA, UMR-6614, CNRS, INSA, University of Normandy, 76000Rouen, France
*
†Email address for correspondence: abdellah.hadjadj@insa-rouen.fr
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Abstract

A new analytical model is derived based on physical concepts and conservation laws, in order to evaluate the post-shock gas velocity, the gas density and the spray dispersion topology during the interaction of a shock wave and a water spray in a one-dimensional configuration. The model is validated against numerical simulations over a wide range of incident Mach numbers $M_s$ and particle volume fractions $\tau _{v,0}$. Two regimes of shock reflection have been identified depending on $M_s$, where the reflected pressure expansion propagates either opposite to the incident shock-wave direction for weak incident Mach numbers or along with it for strong Mach numbers. The numerical simulations reveal the presence of a particle number-density peak for $M_s > 2$ and with particle diameters of the order of ${O}(10)\ \mathrm {\mu } \textrm {m}$. The formation of the number-density peak is discussed and a necessary condition for its existence is proposed for the first time.

JFM classification

Compressible Flows: Gas dynamics Compressible Flows: Shock waves Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 905 , 25 December 2020 , A24
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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